Method and system for automated location dependent probabilistic tropical cyclone forecast

ABSTRACT

A method for automated location dependent probabilistic tropical cyclone forecast. A plurality of new data records representative of alternative tracks are generated based on historical tracks by a first MonteCarlo-module. Points of the new data records are generated from points along the historical track by a dependent sampling process, whereas an intensity climatology is generated, based upon intensity data associated with at least some of the plurality of points along the historical tracks located within a certain grid cell. New intensity data are generated by a second MonteCarlo-module, from the intensity data associated with at least some of the plurality of points along the historical tracks by a MonteCarlo sampling process.

This invention relates to a method and system for automated locationdependent probabilistic tropical cyclone forecast, whereas data recordsof tropical cyclone events are generated and location dependentprobability values for specific weather conditions associated with thetropical cyclone are determined. In particular, the invention relatesall kind of tropical cyclones as e.g. hurricanes, typhoons and tropicalstorms.

Each year, tropical cyclones (also referred to as hurricanes, typhoonsand tropical storms etc.) cause severe damage in various parts of theworld. The occurrence of such weather events is difficult, if notimpossible, to predict over the long term. Even the path, or track, ofan existing storm can be difficult to predict over a period of hours ordays. In particular, the given examples in this document addresshurricanes, whereas typhoons and tropical storms etc. can be treated inthe same manner. Hurricanes is the most severe category of themeteorological phenomenon known as the “tropical cyclone.” Hurricanes,as all tropical cyclones, include a pre-existing weather disturbance,warm tropical oceans, moisture, and relatively light winds aloft. If theright conditions persist long enough, they can combine to produce theviolent winds, incredible waves, torrential rains, and floods weassociate with this phenomenon. So, the formation of a tropical cycloneand its growth into e.g. a hurricane requires: 1) a pre-existing weatherdisturbance; 2) ocean temperatures at least 26° C. to a depth of about45 m; and 3) winds that are relatively light throughout the depth of theatmosphere (low wind shear). Typically, tropical storms and hurricanesweaken when their sources of heat and moisture are cut off (such ashappens when they move over land) or when they encounter strong windshear. However, a weakening hurricane can reintensify if it moves into amore favorable region. The remnants of a landfalling hurricane can stillcause considerable damage. Each year, an average of ten tropical stormsdevelop over the Atlantic Ocean, Caribbean Sea, and Gulf of Mexico. Manyof these remain over the ocean. Six of these storms become hurricaneseach year. In an average 3-year period, roughly five hurricanes strikee.g. the United States coastline, killing approximately 50 to 100 peopleanywhere from Texas to Maine. Of these, two are typically majorhurricanes (winds greater than 110 mph). As mentioned a hurricane is atype of tropical cyclone, which is a generic term for a low pressuresystem that generally forms in the tropics. The cyclone is accompaniedby thunderstorms and, in the Northern Hemisphere, a counterclockwisecirculation of winds near the earth's surface. Tropical cyclones can beclassified as follows: (i) Tropical Depression: An organized system ofclouds and thunderstorms with a defined surface circulation and maximumsustained winds (Sustained winds are defined as a 1-minute average windmeasured at about 10 meters above the surface) of 33 kt or less (1knot=1 nautical mile per hour or 1.15 statute miles per hour); (ii)Tropical Storm: An organized system of strong thunderstorms with adefined surface circulation and maximum sustained winds of 34-63 kt;(iii) Hurricane: An intense tropical weather system of strongthunderstorms with a well-defined surface circulation and maximumsustained winds of 64 kt or higher. Hurricanes are categorized accordingto the strength of their winds using the Saffir-Simpson Hurricane Scale.A Category 1 storm has the lowest wind speeds, while a Category 5hurricane has the strongest. These are relative terms, because lowercategory storms can sometimes inflict greater damage than highercategory storms, depending on where they strike and the particularhazards they bring. In fact, tropical storms can also producesignificant damage and loss of life, mainly due to flooding. Normally,when the winds from these storms reach 34 kt, the cyclone is given aname. It should be mentioned, that the category of the storm does notnecessarily relate directly to the damage it will inflict. Lowercategory storms (and even tropical storms) can cause substantial damagedepending on what other weather features they interact with, where theystrike, and how slow they move.

As mentioned the Saffir-Simpson Hurricane Scale (SS-Scale) defineshurricane strength by categories. A Category 1 storm is the weakesthurricane (winds 64-82 kt); a Category 5 hurricane is the strongest(winds greater than 135 kt). Relating to the caused damage, it can besaid, that typically Category 1 storms with winds between 64-82 kt cancause normally no real damage to building structures. Damages areprimarily to unanchored mobile homes, shrubbery, and trees. There can bealso, some coastal flooding and minor pier damage. Category 2 stormswith winds between 83-95 kt can cause normally some roofing material,door, and window damage. There can also be considerable damage tovegetation, mobile homes, etc. or flooding damages piers and small craftin unprotected moorings may break their moorings. Category 3 storms withwinds between 96-113 kt can cause normally some structural damage tosmall residences and utility buildings, with a minor amount ofcurtainwall failures. Mobile homes are destroyed. Also, flooding nearthe coast destroys smaller structures with larger structures damaged byfloating debris. Terrain may be flooded well inland. Category 4 stormswith winds between 114-135 kt can cause normally more extensivecurtainwall failures with some complete roof structure failure on smallresidences. There can be also major erosion of beach areas. Terrain maybe flooded well inland. Finally Category 5 storms with winds between135+ kt can cause normally complete roof failure on many residences andindustrial buildings. There can be some complete building failures withsmall utility buildings blown over or away. Flooding causes major damageto lower floors of all structures near the shoreline. Massive evacuationof residential areas may be required.

Nevertheless, insurance companies and other entities need to developways of assessing the risks associated with such weather events, andfactoring that knowledge into the pricing of insurance products and themagnitudes and frequencies of damages to expect over time. Informationis available for use in this regard in the form of historical data onstorms which have occurred through the years. Approximately 80 suchstorms occur worldwide each year. Data are collected on many of thesestorms, including positional data for the storm path or “track,” windspeeds, barometric pressures, and other factors. Such storms are bestdocumented in the North Atlantic (i.e., the portion of the AtlanticOcean north of the equator), where reliable data for more than 100 yearsof activity are available. Approximately 10 storms occur in the NorthAtlantic region on an annual basis. Historical data are also availablefor cyclones occurring in the Northwest Pacific, where approximately 26storms occur each year. Suitable data for these Pacific storms areavailable only for the last approximately 50 years. Less data areavailable for storms in other regions.

Using all available historical data, information relating to a fewhundred storms is available for review by researchers and scientists.Such information is useful in assessing risks associated with stormdamages in the subject areas. However, given the unpredictable nature ofstorm behaviour, and the number of factors influencing such behaviours,the available data set of historical storms is relatively small from aprobabilistic viewpoint. Given that this data set will grow by only arelatively few storms per year, a problem exists with regard toperforming statistical analysis relating to the possibility of a stormoccurring at a particular location.

One manner in which this problem can be addressed is by generation ofsimulated or “alternative” storms, and using data from such “storms” toexpand the data set available from historical records. This approach canresult in the availability of thousands, or even tens or hundreds ofthousands, of additional storms from which to create data sets largeenough to perform reliable statistical analyses. The subject inventionis directed to various embodiments involving uses of method, a systemand a computer program product for generating such expandedprobabilistic data sets.

Therefore it should be pointed out that, besides the method according tothe invention, the present invention also relates to a system and acomputer program product for carrying out this method.

In particular the objects are achieved through the invention in that forautomated location dependent tropical cyclone forecast data records ofweather events are generated and location dependent probability valuesfor specific weather conditions associated with the tropical cyclone aredetermined; whereas data records representative of an historical trackof a weather event are assigned to a year of occurrence of said weatherevent and are saved on a memory module of a calculating unit, said datarecords including a plurality of points representative of geographicalpositions and/or intensity of the event along the historical track;whereas a plurality of new data records representative of alternativetracks are generated for each historical track by means of aMonteCarlo-module, wherein points of said new data records are generatedfrom said points along the historical track by a dependent samplingprocess; whereas a grid over a geographical area of interest isestablished by means of the calculation unit, said area including atleast a portion of the plurality of historical tracks, and a intensityclimatology for selected cells in the grid is generated, based upon theintensity data associated with at least some of the plurality of pointsalong the historical tracks located within said selected grid cells;whereas for each of said alternative tracks one or more new intensitydata are generated by means of a second MonteCarlo-module, wherein theone or more new intensity data of the new data records of saidalternative tracks are generated from the intensity data associated withat least some of the plurality of points along the historical tracks bya MonteCarlo sampling process; whereas a distribution for a definabletime period of the data records of the historical tracks is generates bymeans of a scaling table classifying the weather events by intensityand/or year of occurrence, and said distribution of said historicaltracks are reproduced by a filtering module within the new or cumulateddata records according to their assigned year; and whereas a wind fieldof each data record is generated based on a definable wind fieldprofile, and a probability is assigned by a interpolation-module to eachpoint in said grid, giving the probability of the occurrence of aspecific wind strength at a given geographical location and time. Asbasis for the scaling table the Saffir-Simpson Hurricane Scale can forexample be used. The first and second MonteCarlo-module as well as theinterpolation-module can be realized by hardware and/or software.

One embodiment of the invention comprises a method for generating aprobabilistic data set relating to a weather event, such as a tropicalcyclone, or hurricane, typhoon, or tropical storm. This embodiment ofthe method includes the steps of inputting data representative of anhistorical track of a weather event and generating data representativeof a plurality of alternative tracks based on the historical track. Thedata points representative of the alternative tracks are generated fromrespective points along the historical track by a dependent samplingprocess. In certain embodiments, the dependent sampling process is adirected random walk process.

In one embodiment, the step of generating data representative ofalternative tracks based on the historical track comprises the steps ofgenerating a series of random tuples (x_(r),y_(r)) for a historicalpoint (x,y) of the historical track, calculating a sum of randomdeviations (x′,y′) of the random tuples along the historical track, andadding the sum of random deviations (x′,y′) to the historical point(x,y) of the historical track to produce alternative points along thealternative tracks.

The data representative of the historical track(s) include a pluralityof points representative of geographical positions along the historicaltrack(s). The generated data representative of a plurality ofalternative tracks includes a plurality of alternative pointsrepresentative of geographical positions along the alternative tracks.In one embodiment, at least some of the plurality of alternative tracksassociated with a particular historical track have starting points thatdiffer from a starting point of the historical track upon which thealternative tracks are based. The data representative of the historicaltrack may comprise longitude and latitude data to define a location ofeach of a plurality of points.

In certain embodiments of the method, the step of inputting datarepresentative of an historical track includes the step of inputting atleast one of: longitude and latitude of a plurality of pointsrepresentative of the historical track; an azimuth angle for at leastsome of the points along the historical track; celerity for at leastsome of the points along the historical track; a rate of change ofazimuth angle for at least some of the points along the historicaltrack; and a rate of change of celerity for at least some of the pointsalong the historical track. Alternatively, the latter values (azimuth,celerity, and rates of change of azimuth and celerity) may be calculatedfrom longitude and latitude data recorded at periodic time intervals.

Some embodiments of the subject method further comprise the step ofselecting a subset of the data representative of the alternative tracksfor use in the probabilistic data set. In these or other embodiments,the step of generating data representative of alternative tracksincludes the step of limiting a variance of the alternative points froma respective historical point in accordance with one or more physicallaws.

In certain embodiments of the subject method, the step of inputting datarepresentative of a track of an historical weather event includesinputting data representative of an intensity of the event. The datarepresentative of intensity may comprise atmospheric pressure dataassociated with at least some of the plurality of points along thehistorical track. The atmospheric pressure data defines an historicalpressure profile of the historical track. The atmospheric pressure datamay include an absolute pressure and a derivative of (or change in)absolute pressure with respect to time. In certain embodiments, theatmospheric pressure data includes one or more pressure distributions.In some embodiments of the subject method, the step of inputting dataincludes inputting data representative of a plurality of historicaltracks, and the step of establishing a grid over a geographical area ofinterest including at least a portion of the plurality of tracks. Theseembodiments may further comprise the step of establishing a pressureclimatology for selected cells in the grid, based upon the atmosphericpressure data associated with at least some of the plurality of pointsalong the historical tracks located within the selected grid cells. Thepressure climatology for the selected cells may be a pressuredistribution function. The pressure climatology for a selected cell inthe grid may be established from the atmospheric data associated withthe selected cell and/or the atmospheric pressure data associated withone or more cells adjacent the selected cell (i.e., one or moreneighboring cell). In certain embodiments, the pressure climatology fora selected cell is established from a weighted averaging of pressuredata associated with the selected cell and pressure data associated withone or more neighboring cell.

In certain embodiments, each cell in the grid is assigned a land/seavalue. In these embodiments, pressure data associated with an adjacentcell is used to establish the pressure climatology of the selected cellonly if the adjacent and the selected cell have the same land/sea value.

Certain embodiments of the subject method comprise the additional stepof generating one or more alternative pressure profiles for one or moreof the historical tracks using the pressure climatology for the selectedcells in the grid. In addition, one or more pressure profiles may begenerated for one or more of the alternative tracks. One or morealternative pressure profiles may also be generated for one or more ofthe alternative tracks using the pressure climatology for the selectedcells of the grid. In some embodiments, at least one of the alternativepressure profiles for the historical tracks, the pressure profiles forthe alternative tracks, and the alternative pressure profiles for thealternative tracks are modified based, at least in part, on thehistorical pressure profile along the historical track of the associatedweather event.

In certain embodiments of the invention, the step of inputting dataincludes inputting data representative of a plurality of historicaltracks and inputting data representative of atmospheric pressureassociated with at least some of the plurality of points along thehistorical tracks. The atmospheric data defines historical pressureprofiles of the historical tracks. In these embodiments, the step ofgenerating data includes generating a plurality of alternative tracksfor more than one of the historical tracks. Further, these embodimentsinclude at least one of the following steps: a) generating one or morealternative pressure profiles for one or more of the historical tracks;b) generating one or more pressure profiles for one or more of thealternative tracks; and c) generating one or more alternative pressureprofiles for one or more of the alternative tracks. These or otherembodiments of the subject method may further comprise the step ofextracting a subset of data from the data representative of thehistorical tracks, the alternative tracks, and the pressure profiles,based on climatological conditions for a selected time period.

Additional features and advantages will become apparent to those skilledin the art upon consideration of the following detailed description ofillustrative embodiments exemplifying the best mode of carrying out themethod as presently perceived.

The present disclosure will be described hereafter with reference to theattached drawings which are given as non-limiting examples only, inwhich:

FIG. 1 is a flow chart which illustrates the overall operation of oneembodiment of the method of the present invention.

FIG. 2 is a flow chart which further illustrates the step of inputtingdata for historical storms in the embodiment of FIG. 1.

FIG. 3 is a flow chart which further illustrates the step ofestablishing a climatology in the embodiment of FIG. 1.

FIG. 4 is a flow chart which further illustrates the step of producingalternative storm tracks in the embodiment of FIG. 1.

FIG. 5 is a flow chart which further illustrates the step of producingalternative pressure evolutions in the embodiment of FIG. 1.

FIG. 6 is a flow chart which further illustrates the steps of selectinga subset of alternative storms and calculating the wind field in theembodiment of FIG. 1.

FIG. 7 illustrates a method of generating points of a probablistic dataset which are representative of a portion of an alternative storm track.

FIG. 8 a illustrates a plurality of alternative storm tracks generatedby the method of FIG. 7 using a normally-distributed random walk.

FIG. 8 b illustrates a plurality of alternative storm tracks generatedby the method of FIG. 7 using an evenly-distributed random walk.

FIG. 8 c illustrates a plurality of alternative storm tracks generatedby the method of FIG. 7 using a directed random walk.

FIG. 9 a illustrates a plurality of alternative storm tracks, eachoriginating at the starting point of a respective historical track.

FIG. 9 b illustrates a plurality of alternative storm tracks, eachoriginating at an alternative starting point relative to a respectivehistorical track.

FIG. 10 illustrates a plurality of historical and alternative stormtracks superimposed over a portion of a map.

FIG. 11 (a, . . . ,i) illustrates a plurality of alternative pressureevolutions for each of a plurality of storms.

FIG. 1 is a flow chart which illustrates the overall operation of oneembodiment of the subject method. The first step in this embodiment isinputting data for a plurality of historical storms. This step isrepresented by block 12 of FIG. 1. Such data includes geographicalinformation defining the tracks of the respective historical storms andintensity data to indicate the strength of the storm. One source of suchdata is the National Hurricane Center (“NHC”) which is part of theNational Oceanic and Atmospheric Administration (“NOAA”). Geographic andintensity data for hurricanes and tropical cyclones and storms may beviewed at, and is available from, the NHC website at www.nhc.noaa.gov.Following the inputting of this data, a climatology is established inthe area of interest. This operation is represented by block 14 inFIG. 1. After establishment of the climatology, alternative storm tracksare produced for each of the historical tracks in the inputted data.This step is represented by block 16.

Following production of the alternative storm tracks, a plurality ofalternative pressure evolutions are produced for the historical andalternative tracks. This step is represented in FIG. 1 by block 18.Production of the alternative storm tracks, and the alternative pressureevolutions for the historical and alternative tracks, creates arelatively large universe of storms (both historical and alternative). Asubset of the alternative storms is selected based on climatologicaldata. This step is represented by block 20. Finally, wind fields arecalculated for specific points of interest. This step is represented inthe flow chart of FIG. 1 by block 22. Each of steps 12-22 are discussedin additional detail below in connection with the flow charts of FIGS.2-6.

FIG. 2 is a flow chart which further illustrates the step of inputtingdata for historical storms in the embodiment of FIG. 1. The firstoperation in this step is represented by block 24 labeled “Read RawData.” As previously indicated, one source of data on historical stormsis the National Hurricane Center. These data include geographical (i.e.,latitude and longitude) data which define individual nodes of thehistorical track. The locations of storms are generally reported at sixhour time intervals. In many instances, intensity data is also providedin the form of a pressure measurement taken in the vicinity of thecenter of the node. In the event a central pressure measurement is notprovided, a pressure may be calculated from the maximum sustained windalso available on the site. These operations are represented by decisionblock 26 and processing block 28.

After reading the raw data and, if necessary, calculating pressures,additional calculations are performed to determine celerity, azimuthangles and Saffir-Simpson classes. These calculations are represented inthe flow chart of FIG. 2 by block 30. At this point, the data arechecked and verified (block 32). After those operations, the originaldata may be interpolated to enhance resolution. That is, additionalgeographical points or nodes may be defined between the “six hour nodes”available in the raw data. The six hour nodes are interpolated to allowfor a better geographical resolution. In one embodiment, the data areinterpolated to 0.2 degree steps. Such interpolation allows for thegeneration of smoother, alternative storm tracks, and enhances theoverall operation of the subject method. This operation is representedby block 34 of FIG. 2.

The last operation in the step of inputting historical data relates tothe addition of “on-land” flags. When a storm moves from a position overwater to a position over land (or vice versa), substantial pressurechanges are observed. Accordingly, landfall and land leave points aredetermined and entered into the data for use in subsequent steps of theprocess. This operation is represented in the embodiment of FIG. 2 byblock 36.

FIG. 3 is a flow chart which further illustrates the step ofestablishing a climatology in the embodiment of FIG. 1. Even thoughrecords of more than 100 years of reliable pressure data exist, thishistorical data is preferably preprocessed in order to obtain a moreconsistent database by the methods described herein. The first operationin the step of establishing a pressure climatology is establishment of a1° by 1° grid over the geographical area of interest. This operation isrepresented by step 38 in the embodiment of FIG. 3. The original dataincludes both the absolute pressure at specified locations, and thechange in pressure (i.e., the pressure derivative). These data arematched with the individual grid locations (block 40). Some locations inthe grid will have many observed pressure and pressure derivativevalues. Other locations have fewer observed values, and yet others mayhave none.

Following this operation, minimum pressures based on the sea surfacetemperature (SST) climatology are added. That is, for each location inthe grid, the lowest pressure associated with the highest SST everobserved in that particular location is entered. This value acts as a“floor” for alternative pressure values associated with each location inthe grid that may be selected (as discussed in additional detail below)in connection with alternative pressure evolutions for the historicaland/or alternative storm tracks. This operation is represented by block42 in the embodiment of FIG. 3.

After addition of minimum pressures, the pressure climatology issmoothed. The goals of the smoothing process include one or more of thefollowing: to obtain full coverage of the area of interest; to smoothvariations in the distributions of pressures and pressure derivativesfrom one grid to its neighboring grids; to smooth variations indistributions of minimums, maximums and means of the absolute pressuresand pressure derivatives; and to obtain the same number of“observations” at each grid location. This smoothing process leads to amore consistent set of pressure related values for the area of interestto be used in a sampling process to be described further below. In theparticular embodiment being described, the quantities to be smoothed arenot scaler quantities (such as, a mean pressure quantity at eachlocation), but rather are pressure-related distributions for eachlocation. Accordingly, the smoothing process is relatively more complex.

In order to achieve the goals stated above, one embodiment of thesubject method follows the approach set forth below. Other approachesmay be used, and some may very well be comparable to, or even preferredover, this approach. The approach is as follows:

The number of valid observations at each location is determined. In thisembodiment, up to 260 observations for each location may be entered.Some locations may have this many observations (or more) while otherlocations may have fewer or none. All non-valid data are replaced. Thedistinction between valid observations and non-valid observations isbased upon the fact that pressure values below 800 hPa are impossible,and thus not valid. After all valid observations are entered for eachlocation, the subject method loops through the data location, applyingthe following procedure at each location (referred to as the “centerlocation”):

1) Obtain all valid observations for the center location and allneighboring locations (i.e., all grid cells surrounding the “center”cell) having the same land/sea value. That is, if the center location isa sea location, only neighboring locations that are also sea locationsare considered. If the center location is a land location, onlyneighboring locations that are also land locations are considered. Thus,land and sea observations are not mixed in the smoothing process.

2) Construct the pressure distribution file for all points. The centerlocation observations are more heavily weighted, for example, bycounting them twice. Depending on the number of neighboring locationshaving the same land/sea values and the number of valid observations ateach location, an arbitrary number of observations for this particularpressure distribution file is obtained.

3) Use a cubic spline to interpolate the pressure distribution functionto a standard number of observations (for example, 100 observations foreach location).

The above approach will produce a data set having a standard number (forexample, 100) of pressure and pressure derivative observations at eachgrid cell which is not separated by more than 1 degree from an originalcell. By iteration, one can in theory fill all gaps existing in the areaof interest.

The above-described approach accomplishes the goals set forthpreviously. Locations in which historical observations are not availablewithin the area of interest are “filled in,” and variations across thearea of interest are smoothed. However, sharp pressure gradients whichoccur at land/sea transition locations are maintained.

The pressure climatology smoothing operation is represented in FIG. 3 byblock 44. It should be noted that, in the described embodiment, both aland climatology and a sea climatology are established and smoothed inthe manner described above.

FIG. 4 is a flow chart which further illustrates the step of producingalternative storm tracks in the embodiment of FIG. 1. The first step inthis operation is selection of one of the plurality of historical tracks(i.e., longitude and latitude data) inputted in the first step of theoverall process illustrated in FIG. 1. The selection operation isrepresented in the flow chart of FIG. 4 by block 46. An alternativetrack is then generated for the selected historical track. The specificmanner in which each alternative track is generated is described inadditional detail below. This operation is represented in the flow chartof FIG. 4 by block 48. A plurality (N) of alternative tracks areproduced. In the embodiment of FIG. 4 this is illustrated by thepresence of decision block 50 and the resulting loop. Similarly, aplurality of tracks are generated for each historical track. This aspectof the operation is illustrated by the presence of decision block 52 andthe resulting loop.

Following generation of the alternative tracks, the embodiment of themethod illustrated in FIG. 1 produces an alternative pressure evolution(“APE”) for each of the historical tracks and the alternative tracks.FIG. 5 is a flow chart which further illustrates the step of producingAPEs in the embodiment of FIG. 1. The first operation in this step isselection of an historical track. This operation is represented in FIG.5 by block 54. The next operation in this step is generation of an APEfor a selected historical track. This operation is represented in FIG. 5by block 56. A plurality (M) of APEs are generated. This feature isrepresented schematically by decision block 58, and the resulting loop.

In addition to generating an APE for each historical track, it isdesirable to generate an APE for each alternative track associated witheach historical track. Accordingly, after generation of an APE for thefirst historical track, the method of this embodiment associates eachalternative track generated from the selected historical track with theoriginal pressure evolution of the historical track. This operation isrepresented in FIG. 5 by block 60. An APE is then generated for thealternative track (block 62). The methodology for generating the APE isthe same as was used in connection with the operation referred to inconnection with block 56. A specific sampling process applicable to thisoperation is discussed in additional detail below. A plurality (M) ofAPEs are generated for each alternative track. This feature isillustrated in FIG. 5 by decision block 64, and the resulting loop. APEsare then similarly generated for each of the plurality (N) ofalternative tracks associated with each historical track. This featureis illustrated by decision block 66 in FIG. 5, and the resulting loop.Finally, the operation continues in this manner until APEs have beengenerated for all historical tracks and all associated alternativetracks. This feature is illustrated in the embodiment of FIG. 5 bydecision block 68, and the resulting loop.

FIG. 6 is a flow chart which further illustrates the steps of selectinga subset of alternative storms based on climatology in the embodiment ofFIG. 1. The first operation in this step is selection of alternativetracks to create a plurality of “clone” years. Specifically, eachhistorical year includes a plurality of historical storms. In accordancewith the above discussion, a plurality (N) of alternative tracks arecreated for each historical track in a given year. However, since thealternative tracks are produced by a random process (albeit one thatuses a dependent sampling technique), some of the alternative tracks fora given year are more likely to occur than others. The selection processis based upon knowledge of the climatology for the actual year in whichthe associated historical storm tracks occurred. In other words,alternative tracks which might be judged as relatively unlikely to occurin actuality are deselected, based on established climatologicalknowledge. Thus, from the universe of alternative tracks available tocreate a “clone” year, a selection is made to include certain of thealternative tracks and exclude others. This operation is illustrated byblock 70 in FIG. 6.

An “adjustment” made to the data for the selected storms relates to thepreviously discussed “on-land” flags. Since pressures increase rapidlywhen a storm moves from over water to over land, pressure dataassociated with the alternative tracks are adjusted to reflect thisphenomena. This operation is represented by block 72 in the flow chartof FIG. 6.

The final step in the overall methodology illustrated by the flow chartof FIG. 1 relates to calculation of the wind field for particular pointsalong each storm path. Such calculations include application ofHolland's Formula, accounting for directional roughness values, andaccounting for extra-tropical transitions. These operations arerepresented by blocks 74, 76, 78, and 80 in the flow chart of FIG. 6.

As previously noted, the alternative storm tracks are generated by adependent sampling technique. FIG. 7 illustrates a method of generatingpoints of a probabilistic data set which are representative of analternative storm track. With reference to FIG. 7, line segment 100represents a portion of an historical storm track. For purposes ofdiscussion, an x-y coordinate system has been superimposed such thatline 100 may be represented by three points, as follows:

x = 0 1 2 y = 0 1 1

Corresponding points of an alternative track, represented by line 102,are produced by generating a series of random tuples (x_(r),y_(r)) foreach point of the historical track, then calculating the cumulative sum(x′,y′) of these random numbers along the track (i.e., summing up randomdeviations along the track), and then adding these accumulated randomdeviations (x′, y′) to the historical track (x,y). The resulting pointsdefine the alternative track. In the example of FIG. 7, the randomtuples are:

x_(r) = 1 0 −1 y_(r) = 0 0 1

The cumulative sums along the alternative track are:

x′ = 1 1 + 0 = 1 1 + (−1) = 0 y′ = 0 0 + 0 = 0 0 + 1 = 1

Finally, the points on the generated track (line 102) are obtained asfollows:

x + x′ = 0 + 1 = 1 1 + 1 = 2 2 + 0 = 2 y + y′ = 0 + 0 = 0 1 + 0 = 1 1 +1 = 2

There are different ways to generate the random numbers, either byindependently sampling from a normal or uniform distribution, or by adependent sampling technique (such as, a directed random walk). Usingthe latter, a subsequent point can only deviate to a certain degree froma previous point. As will be illustrated in additional detail below, adependent sampling technique (particularly, a directed random walk)generates more realistic alternative storm tracks.

FIGS. 8 a-8 c illustrate alternative storm tracks generated by theabove-described technique, using both independent and dependentsampling. FIG. 8 a illustrates the results achieved when the randomnumbers are generated by independent sampling from a normaldistribution. In FIG. 8 a, heavy line 104 represents the historicaltrack. The remaining lines represent alternative tracks. The alternativetracks illustrate erratic storm movements which are not likely to occurin nature.

FIG. 8 b shows historical track 104 and a plurality of alternativetracks generated by an independent sampling technique wherein the randomnumbers are generated from a uniform distribution. The alternativetracks in this example are much smoother than those illustrated in FIG.8 a. However, the alternative tracks in FIG. 8 b continue to exhibitunrealistic “movements” at numerous points along the track.

FIG. 8 c shows historical track 104 and a plurality of alternativetracks generated by a dependent sampling technique. In FIG. 8 c, eachpoint along an alternative track can only deviate to a certain degreefrom the previous point. As the results illustrate, this “directedrandom walk” generates alternative tracks which are more realistic thanthose illustrated in FIGS. 8 a and 8 b.

FIG. 9 a illustrates the results produced when a plurality ofalternative tracks are generated from each of a relatively larger numberof historical tracks. In the illustration of FIG. 9 a, each historicaltrack, and its respective associated alternative tracks, begins at acommon point (see, for example, the tracks beginning in the lower rightportion of FIG. 9 a). FIG. 9 b illustrates a similar number of tracks,but incorporates a refinement that is an aspect of the presentinvention. The refinement involves selecting alternative starting pointsfor each of the plurality of alternative tracks associated with aparticular historical track. The effects of this change are readilyapparent by the differences in the lower right portions of FIG. 9 a andFIG. 9 b, respectively. This change alleviates somewhat an unnatural“clustering” of alternative and historical tracks which is apparent inthe illustration of FIG. 9 a.

FIG. 10 illustrates the result which is obtained when a relatively largenumber of historical tracks, and a plurality of alternative tracksassociated with each historical track, are superimposed upon a map ofthe Caribbean and North Atlantic.

The sampling process by which the alternative pressure evolutions (APEs)are produced will now be described. As discussed above in connectionwith FIG. 3, a pressure climatology is established and smoothed.Subsequent to these steps, an historical storm is selected for sampling.At each location, the historical pressure is first noted. Then, analternative pressure value is selected from the pressure distributionsavailable for that location from the smoothed pressure climatology. Thechosen pressure is then associated with that geographical point of thehistorical track to produce an alternative pressure evolution for thatpoint. This process is repeated to create a plurality (M) of alternativepressure values for each point, and thus a plurality of alternativepressure evolutions for the historical track.

One manner of producing an alternative pressure evolution for a selectedtrack may be referred to as the “minimum” method. In this method, thelocation (latitude and longitude) of the absolute pressure minimum inthe selected track is identified. A new pressure value is then selectedaccording to a pressure distribution function at that location. Theselection may be based on a random choice. Once the new minimum value ischosen, all other pressure values along the selected track are adjustedaccordingly, leaving only the first and last values unchanged. Thisresults in an alternative pressure evolution which mirrors the shape ofthe selected track, but in which the absolute values of the pressureswill vary at each location (except for the very first and very lastlocations along the track). Landfall and landleave locations may also beidentified to assure that appropriate values are set in the alternativepressure evolutions at these locations.

Another method by which alternative pressure evolutions may be generatedcan be described as the “percentile” method. This method is based onpressure differences over time (dp/dt), along with information from thehistorical track. The steps for computing a pressure evolution for analternative track are as follows:

a) At time t=0 along the alternative track, the pressure value p(0) isset equal to the pressure value of the historical storm at time t=0.

b) At time t=1, the pressure value along the alternative track isdetermined by first determining the percentile of the pressure changealong the historical track between times t=0 and t=1. This value islocated on the pressure distribution curve for the historical track atlocation x=1. The percentile is varied by a certain amount, and apressure change value corresponding to the varied percentile is locatedin the pressure distribution for location x=1 of the alternative track.The pressure value at time t=1 in the alternative track is then equal tothe pressure at time t=0 plus the value located in the alternative trackpressure distribution.

c) The above steps are repeated for time t=2, with reference back to thevalues determined at time t=1.

The percentile is preferably varied according to a uniform distribution.Variance is preferably approximately plus/minus 15%. A secondalternative pressure evolution may be created by starting from the lasttime step and following the same procedure working in reverse to timet=0. A third alternative pressure evolution may be determined by takinga weighted average of the first and second pressure evolutions, givingmore weight to the first near the beginning of the track and more weightto the second near the track's end. It will be appreciated by those ofskill in the art that other variations may be similarly determined toproduce additional pressure evolutions.

The process of generating alternative pressure evolutions is repeatedfor each of the historical tracks inputted in the initial step, and foreach of the alternative tracks generated from each of the historicaltracks. Thus, if there are N alternative tracks generated for eachhistorical track, and if there are M APEs generated for each of thehistorical and alternative tracks, a total of (N+1)×M “artificial”storms are generated for each historical storm for which data areavailable That is, each track (whether it is a historical or analternative one) is associated with M hypothetical pressure evolutions.

FIG. 11 illustrates APEs generated for a plurality of storm tracks. Ineach of the illustrations of FIG. 11, the pressure evolution of aselected storm track is illustrated by a dark line, while APEs generatedfor the selected storm track are represented by lighter lines. Aspreviously discussed, the profiles or shapes of the APEs are similar tothe selected track. However, the absolute pressure values at any givenlocation along the track differ, as illustrated.

The choice of alternative pressures for each point of the historicalpressure evolution is subject to some constraints. For example, thealternative pressure value chosen for a particular point will not exceedpressure values that have never been observed at that particular point,or those that have been determined using the extension of theclimatology based on the SST. Furthermore, if in the historical pressureevolution, an unusual pressure variation occurs at a particularlocation, then similarly unusual variations may be selected for the APEsat that location. Pressure variations which are not possible in nature,or would be extremely unlikely to occur at a given location, are alsoavoided. The pressure distributions developed in connection with theestablishment of the pressure climatology discussed in connection withFIG. 3 are used to facilitate satisfaction of these constraints.

Although the present disclosure has been described with reference toparticular means, materials and embodiments, from the foregoingdescription, one skilled in the art can easily ascertain the essentialcharacteristics of the present disclosure and various changes andmodifications may be made to adapt the various uses and characteristicswithout departing from the spirit and scope of the present invention asset forth in the following claims.

1. A method for automated location dependent probabilistic tropicalcyclone forecast in which data records of weather events are generatedand location dependent probability values for specific weatherconditions associated with the tropical cyclone are determined,comprising: assigning data records representative of an historical trackof a weather event to a year of occurrence of said weather event andsaving the data records on a memory module of a calculating unit, saiddata records including a plurality of points representative ofgeographical positions and/or intensity of the event along thehistorical track; generating a plurality of new data recordsrepresentative of alternative tracks for each historical track using afirst MonteCarlo-module, wherein points of said new data records aregenerated from said points along the historical track by a dependentsampling process; generating a grid over a geographical area of interestusing the calculation unit, said area including at least a portion ofthe plurality of historical tracks, and generating an intensityclimatology for selected cells in the grid based upon the intensity dataassociated with at least some of the plurality of points along thehistorical tracks located within said selected grid cells; generatingfor each of said alternative tracks one or more new intensity data usinga second MonteCarlo-module, wherein the one or more new intensity dataof the new data records of said alternative tracks are generated fromthe intensity data associated with at least some of the plurality ofpoints along the historical tracks by a MonteCarlo sampling process;generating a distribution for a definable time period of the datarecords of the historical tracks using a scaling table classifying theweather events by intensity and/or year of occurrence, and saiddistribution of said historical tracks are reproduced by a filteringmodule within the new or accumulated data records according to theirassigned year; and generating a wind field of each data record based ona definable wind field profile, and assigning a probability by aninterpolation-module to each point in said grid giving the probabilityof the occurrence of a specific wind strength at a given geographicallocation and time.
 2. Method according to claim 1, characterized in,that for the weather events tropical cyclone events, in particularhurricane events or typhoon events or tropical storm events are used. 3.Method according to claim 1, characterized in, that said datarepresentative of intensity comprises atmospheric pressure dataassociated with at least some of the plurality of points along thehistorical track, said atmospheric pressure data defining an historicalpressure profile of the historical track.
 4. Method according to claim3, characterized in, that the intensity climatology comprises a pressureclimatology.
 5. Method according to claim 4, characterized in, that thepressure climatology for at least one of the selected cells is apressure distribution function.
 6. Method according to claim 3,characterized in, that said atmospheric pressure data includes anabsolute pressure (P) and a derivative of absolute pressure with respectto time (dP/dT).
 7. Method according to claim 4, characterized in, thatthe pressure climatology for a selected cell in the grid is establishedfrom at least one of the atmospheric pressure data associated with theselected cell and the atmospheric pressure data associated with one ormore cells adjacent the selected cell.
 8. Method according to claim 4,characterized in, that the pressure climatology for a selected cell isestablished from a weighted averaging of pressure data associated withthe selected cell and pressure data associated with one or more cellsadjacent a selected cell.
 9. Method according to claim 4, characterizedin, that each cell in the grid is assigned a land/sea value, and whereinpressure data associated with an adjacent cell is used to establish thepressure climatology of a selected cell only if the adjacent cell andthe selected cell have the same land/sea value.
 10. Method according toclaim 4, characterized in, that one or more alternative pressureprofiles for one or more of the historical tracks using the pressureclimatology for the selected cells in the grid are generated.
 11. Methodaccording to claim 3, characterized in, that one or more pressureprofiles for one or more of the alternative tracks are generated. 12.Method according to claim 4, characterized in, that one or morealternative pressure profiles for one or more of the alternative tracksusing the pressure climatology for the selected cells of the grid aregenerated.
 13. Method according to claim 3, characterized in, that atleast one of the alternative pressure profiles for the historicaltracks, the pressure profiles for the alternative tracks, and thealternative pressure profiles for the alternative tracks are modifiedbased, at least in part, on the historical pressure profile along thehistorical track of the associated weather event.
 14. Method accordingto claim 1, characterized in, that said dependent sampling process is adirected random walk process.
 15. Method according to claim 1,characterized in, that at least some of the plurality of alternativetracks have starting points that differ from a starting point of thehistorical track upon which said alternative tracks are based. 16.Method according to claim 1, characterized in, that data representativeof alternate tracks based on said historical track are generated by: i)generating a series of random tuples (x_(r),y_(r)) for a historicalpoint (x,y) of the historical track; ii) calculating a sum of randomdeviations (x′,y′) of the random tuples along the historical track; andiii) adding the sum of random deviations (x′,y′) to the historical point(x,y) of the historical track to produce alternative points along thealternative tracks.
 17. Method according to claim 1, characterized in,that a longitude and a latitude are assigned to said data representativeof a track of an historical weather event whereas said longitude andsaid latitude define each of a plurality of points along said track. 18.Method according to claim 1, characterized in, that said data recordsinclude data records representative of a plurality of historic tracks,and said new data records include data records representative aplurality of alternative tracks for more than one of said plurality ofhistorical tracks.
 19. Method according to claim 1, characterized in,that said data representative of an historical track comprises at least:i) longitude and latitude of a plurality of points representative of thehistorical track; ii) an azimuth angle for at least some of the pointsalong the historical track; iii) celerity for at least some of thepoints along the historical track; iv) a rate of change of azimuth anglefor at least some of the points along the historical track; and v) arate of change of celerity for at least some of the points along thehistorical track.
 20. Method according to claim 1, characterized in,that at least one subset of the data representative of the alternativetracks for use in the probabilistic data set is selected.
 21. Methodaccording to claim 1, characterized in, that a variance of saidalternative points of said data records representative of alternativetracks from a respective historical point in accordance with one or morephysical laws is limited.
 22. Method according to claim 1, characterizedin, that said data records comprise data representative of a pluralityof historical tracks and data representative of atmospheric pressureassociated with at least some of the plurality of points along thehistorical tracks, said atmospheric data defining historical pressureprofiles of the historical tracks, and that said new data recordscomprise a plurality of alternative tracks for more than one of saidplurality of historical tracks, whereas: i) One or more alternativepressure profiles for one or more of the historical tracks aregenerated; ii) One or more pressure profiles for one or more of thealternative tracks are generated; and iii) One or more alternativepressure profiles for one or more of the alternative tracks aregenerated.
 23. Method according to claim 22, characterized in, that atleast one subset of data from the data representative of the historicaltracks is extracted, the alternative tracks, and the pressure profiles,based on climatological conditions for a selected time period. 24.Method according to claim 3, characterized in that a plurality ofalternative pressure profiles associated with the track of thehistorical weather event are generated.
 25. Method according to claim24, characterized in that a plurality of alternative pressure profilesis generated by means of the Monte-Carlo module by: (i) Identifying apoint of occurrence of an absolute pressure minimum along the track ofthe historical weather event; (ii) Selecting an alternative pressurevalue at the point identified in step (i); (iii) Adjusting pressurevalues at a plurality of other points along the track of the historicalweather event, in accordance with the selected alternative pressurevalue, to create an alternative pressure profile; and (iv) Repeatingsteps (i), (ii), and (iii) to produce a plurality of alternativepressure profiles associated with the track of the historical weatherevent.
 26. Method according to claim 24, characterized in that datarepresentative of a plurality of alternative tracks are generated basedon said track of the historical weather event, said data including aplurality of alternative points representative of geographical positionsalong said alternative tracks.
 27. Method according to claim 26,characterized in that a plurality of alternative pressure profilesassociated with at least some of said plurality of alternative tracksare generated.
 28. Method according to claim 27, characterized in thatsaid plurality of alternative pressure profiles associated with saidplurality of alternative tracks are generated by: (i) Identifying apoint of occurrence of an absolute pressure minimum along one of saidalternative tracks; (ii) Selecting an alternative pressure value at thepoint identified in step (d); (iii) Adjusting pressure values at aplurality of other points along said alternative track, in accordancewith the selected alternative pressure value, to create an alternativepressure profile; and (iv) Repeating steps (i), (ii), and (iii) toproduce a plurality of alternative pressure profiles associated withsaid plurality of alternative tracks.
 29. Method according to claim 28,characterized in that a plurality of alternative pressure profilesassociated with at least some of the plurality of alternative tracks aregenerated by: (i) Identifying a pressure value at a first position alongthe historical track, and setting a pressure value at a correspondingposition along an alternative track equal to the identified pressurevalue; (ii) Determining a percentile of pressure change along thehistorical track between said first location and a second location;(iii) Varying the percentile by a selected amount; (iv) Determining apressure value at a second location of the alternative track based uponthe varied percentile; (v) Repeating steps (i), (ii), (iii), and (iv)for additional points along the alternative track to create analternative pressure profile associated with the alternative track; and(vi) Repeating steps (i), (ii), (iii), (iv), and (v) to create pressureprofiles for other ones of the plurality of alternative tracks. 30.Method according to claim 28, characterized in that the percentile isvaried by approximately plus/minus fifteen percent.
 31. Method accordingto claim 29, characterized in additional alternative pressure profilesare generated by means of the Monte-Carlo module by: (i) selecting adifferent position along the historical track as a starting point,and/or (ii) varying the percentile by a different amount.
 32. Methodaccording to claim 1, characterized in, that as basis for the scalingtable the Saffir-Simpson Hurricane Scale is used.
 33. A system forautomated location dependent tropical cyclone forecast in which datarecords of weather events are generated and location dependentprobability values for specific weather conditions associated with thetropical cyclone are determined, comprising: a calculation module forassigning data records representative of an historical track of aweather event to a year of occurrence of said weather event and a memorymodule for saving the data records onto, said data records including aplurality of points representative of geographical positions and/orintensity of the event along the historical track; a MonteCarlo-modulefor generating a plurality of new data records representative ofalternative tracks for each historical track, wherein points of said newdata records are generated from said points along the historical trackby a dependent sampling process; the calculation module including meansfor establishing a grid over a geographical area of interest, said areaincluding at least a portion of the plurality of historical tracks, andfor generating a intensity climatology for selected cells in the grid,based upon the intensity data associated with at least some of theplurality of points along the historical tracks located within saidselected grid cells; a scaling table for generating a distribution for adefinable time period of the data records of the historical tracks, thescaling table classifying the weather events by intensity and/or year ofoccurrence, and a filtering module for reproducing said distribution ofsaid historical tracks within the new or accumulated data recordsaccording to their assigned year; and a definable wind field profile forgenerating a wind field of each data record, and a interpolation-modulefor assigning a probability to each point in said grid, giving theprobability of the occurrence of a specific wind strength at a givengeographical location and time.
 34. A computer program product which isable to be loaded in the internal memory of a digital computer andcomprises software code sections with which the steps according to claim1 are able to be carried out when the product runs on a computer.